Construct the Karnaugh maps and find the minimum SOP, and minimum POS expression for each of these logic functions:
a.) ? = ?̅ ?̅?̅ + ?̅ ??̅ + ??̅? + ???
b.) ? = ?̅?̅?̅+ ??̅?̅+ ?̅?̅? + ??̅? + ?̅??
c.) ? = ?̅???̅ + ???̅?̅ + ???̅? + ???
Construct the Karnaugh maps and find the minimum SOP, and minimum POS expression for each of...
(14)Use a Karnaugh map to find the minimum POS for [1 (A+B+C)(A+B+C)(A+B+C) Show the equivalent SOP expression. [10 pts]
Express the following SOP expression a a POS expression using a Karnaugh map and DeMorgan's theorems A middot B middot C middot D + A middot B middot C middot D + A middot B middot C middot D + A middot B middot C middot D + A middot B middot C middot D + A middot B middot C middot D + A middot B middot C middot D + A middot B middot C middot D.
1. Use K-maps to reduce each of the following to a minimized SOP form: (a) A + BC + CD (b) ABCD + ABCD + ABCD + ABCD (c) ABCD + CD) + ABCD + CD) + ABCD (d) (AB + ABXCD + CD) (e) AB + AB + CD + CD 2. Use K-maps to find the minimum SOP expression for the logic function shown in the table to the right. Implement the circuit using NAND gates only. Inputs...
Question 4. (a) Find the minimum sum-of-products expression for each of the functions below using Karnaugh maps i) F = EA,B,C,D(2, 3, 6, 7, 12, 13, 14) (Note: the numbers in the brackets correspond to positions in the Karnaugh map where F takes the logic value 1, ie F = 1 when ABCD = 0010, 0011, 0110, etc). ii) F = []w.x,y,z(0, 2, 6, 7, 8, 14, 15) (Note: the numbers in the brackets correspond to positions in the Karnaugh...
F5.2 Construct a Karnaugh map for the logic function: D = ABC + A'BC + ABC' + BC Find the minimum SOP expression. Realize the function using only NAND gates. [15]
Using Karnaugh maps, find a minimal sum-of-products expression for each of the following logic functions. F_a = sigma_w, x, y, z(0, 1, 3, 5, 14) + d(8, 15) F_b = sigma_w, x, y, z(0, 1, 2, 8, 11) + d(3, 9, 15) F_c = sigma_A, B, C, D (4, 6, 7, 9, 13) + d(12) F_d = sigma_W, X, Y, Z (4, 5, 9, 13, 15) + d{0, 1, 7, 11, 12)
(c) Use a Karnaugh map to reduce the following 4-variable expression to a minimum SOP form. CD(AB+AB)+CD(AB+AB)+CD(AB+ AB)+ ABCD+ABCD+ACD+ACD (5 marks)
Question 2 1. Formulate the minimized SOP and POS Boolean expression for the following truth table using Karnaugh map techniques. Out of the SOP and POS implementations, which is cheaper in terms of number of transistors? You can assume two transistors per input for a gate. (10 points) A B C Output 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1
les K-Map.pdf A (1,0231707 KB) Practice-5 variable K-Map.pdf A (1.868 MB) Use Karnaugh maps to design lowest cost circuits for the following functions with NOT, AND and OR gates. To find the lowest cost, it is a good idea to check both the SOP form of the circuit and POS form of the circuit and compare their cost to find the lowest cost circuit. Hint: Use Karnaugh maps for both SOP and Pos forms and then obtain the simplified expression...
Computer Engineering 3. (3 points) Simplify the following POS expression, giving the result in SOP form. Hint: Use K-maps) Out- (AtB+C+D) (A+B+C+D) (A+B+c+D) (A+B+C+ D) (A+B+C+D) (A+B+C+D) (A B+C+D)